There are ways and means of winning matches in the Premier League and in condemning Southampton to their sixth defeat in seven matches, Slaven Bilic taught Claude Puel a severe lesson.

The Saints have their moments and those moments can be bewitching. Manolo Gabbiadini’s debut goal was one such, the £14m striker smashing home off the bar from an acute angle to give his side a 12th-minute lead. But in certain vital qualities – strength, aggression, determination – they are lacking and after a day of topsy-turvy results Puel is looking over his shoulder at the relegation zone.

For Bilic, meanwhile, it must feel like the storm has cleared. The Croat has seemed a bereft figure at points this season as he has dealt not only with poor form but a new, unpopular home and a series of injuries. But the ostracisation and subsequent departure of Dimitri Payet appears to have been a cathartic moment. The Hammers have now won three of their past four matches and are back in the top half of the table.

“We deserved this big time,” Bilic said after the match. “We closed down, we made tackles, we defended deep when we needed to and then, once we had a goal, we were everything you could ask for. You have a plan but the boys were responsible; they executed that brilliantly.”

The Hammers drew level two minutes after falling behind and Pedro Obiang was the architect. After he was allowed to advance all the way from his own half to within 25 yards of goal, not only did Southampton back off but they failed to close the gaps in midfield and defence. Obiang was able to pick a pass through both lines and find Andy Carroll, who had spun Jack Stephens as if he was not there. Carroll, who left the field in the second half with a tweaked groin that Bilic believes should not keep him out of their next match, calmly took a touch and finished low under Fraser Forster.

The scoreline was even, then, but there was a definite sense that West Ham had the hosts’ measure. Playing physically wherever possible and looking to hit crosses at the young Stephens and uncertain Maya Yoshida, their game plan was clear but Saints were hard pressed to counter it. What is more, with Robert Snodgrass on set-pieces, it was fair to say that the Hammers had quality in delivery to match the departed Payet.

“With Snodgrass, we knew about his left foot, we knew about his vision and the plans he forms in his head,” Bilic said. “But his work rate was amazing.”

It was a Snodgrass corner that led to West Ham’s second goal on the verge of half-time. The ball was swung in to the penalty spot where Gabbiadini met it and flicked it well clear of the area. It fell again to Obiang, however, and he drove the ball straight back at goal. It bobbled and took a small deflection but still should have been saved by Forster, who was unable to stop it. Bilic said it was the crucial moment in the match.

Puel made changes at half-time but introduced Shane Long – who had three goals in his four previous matches – only when Sofiane Boufal went off injured. The Saints created chances, but by that point they were 3-1 down after a Mark Noble free-kick was deflected into the net by Steven Davis.

“We started very well with a fantastic goal and it’s not the first time we’ve conceded within five minutes,” Puel said, whose side travel next to David Moyes’s Sunderland. “We need concentration and we lacked energy in the first half. The second half was quality with many chances, but it’s not good enough only to win the second half.

“We play against teams now that it’s important to take points from. We can see the top half of the table but we can also see other possibilities. It’s an important game against Sunderland.”

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